Evolutionary Model of Stock Markets

TL;DR

This paper introduces an evolutionary model for stock prices, describing short-term distributions and long-term trends using logistic and mixture distributions, and provides a framework for analyzing price competition and long-term market behavior.

Contribution

It develops a novel evolutionary framework for stock market dynamics, linking short-term distributions with long-term trends through a Walrus and replicator equation.

Findings

Short-term price distribution follows a logistic (Laplace) form.

Long-term returns are modeled by Laplace-Gaussian mixtures.

Empirical analysis of two stocks supports the model's predictions.

Abstract

The paper presents an evolutionary economic model for the price evolution of stocks. Treating a stock market as a self-organized system governed by a fast purchase process and slow variations of demand and supply the model suggests that the short term price distribution has the form a logistic (Laplace) distribution. The long term return can be described by Laplace-Gaussian mixture distributions. The long term mean price evolution is governed by a Walrus equation, which can be transformed into a replicator equation. This allows quantifying the evolutionary price competition between stocks. The theory suggests that stock prices scaled by the price over all stocks can be used to investigate long-term trends in a Fisher-Pry plot. The price competition that follows from the model is illustrated by examining the empirical long-term price trends of two stocks.